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Modus Tollens

Modus tollens is a valid argument form in propositional calculus in which p and q are propositions. If p implies q, and q is false, then p is false. This inference rule underlies proof by contrapositive, one form of indirect proof.

(p=>q,¬q)/(∴¬p)

For example, if being the king implies having a crown, not having a crown implies not being the king.

See also

Indirect Proof, Modus Ponens, Proof by Contradiction

This entry contributed by Jordan Bell

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References

Copi, I. M. and Cohen, C. Introduction to Logic. Upper Saddle River, NJ: Prentice Hall, 2001.

Referenced on Wolfram|Alpha

Modus Tollens

Cite this as:

Weisstein, Eric W., with contributions by Jordan Bell. "Modus Tollens." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ModusTollens.html

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